数列{an}各项均为正数,其前n项和为sn,且满足2ansn-an2=1,设bn=2/4sn4-1,求数列{bn}的前n项和Tnan2为an的平方,sn4为sn的4次方

数列{an}各项均为正数,其前n项和为sn,且满足2ansn-an2=1,设bn=2/4sn4-1,求数列{bn}的前n项和Tnan2为an的平方,sn4为sn的4次方
数列{an}各项均为正数,其前n项和为sn,且满足2ansn-an2=1,设bn=2/4sn4-1,求数列{bn}的前n项和Tn
an2为an的平方,sn4为sn的4次方

数列{an}各项均为正数,其前n项和为sn,且满足2ansn-an2=1,设bn=2/4sn4-1,求数列{bn}的前n项和Tnan2为an的平方,sn4为sn的4次方
2anSn-(an)2=1
n=1,a1=1
2[Sn-S(n-1)]Sn-[Sn-S(n-1)]^2=1
(Sn)^2-[S(n-1)]^2 =1
{(Sn)^2} 是等差数列,d=1
(Sn)^2-(S1)^2 = n-1
(Sn)^2 = n
bn=2/[4(Sn)^4-1]
= 2/(4n^2-1)
= 1/(2n-1) - 1/(2n+1)
Tn = b1+b2+...+bn
= 1 - 1/(2n+1)
= 2n/(2n+1)